How to move a tile in OpenTTD

You cannot 'move' any structure you have constructed. The game does not allow you to undo any action, be it construction or purchases.

To move something, you have to build the structure somewhere else, then remove the original. For stations, as long as the new station is within a certain radius of the original and you construct the replacement first, the new station will be grouped together with the original. This may also work for other structures, but further testing is needed.